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dmd an hour ago

Area isn’t notably affected by fractal boundaries. Only perimeter is.

boothby 20 minutes ago | parent [-]

Can you explain this more? It seems trivial to extrude a 2d coastline along a third dimension to produce a paradoxical areal calculation corresponding precisely to the perimeter paradox...

dmd 15 minutes ago | parent [-]

If you extrude a coastline into a wall the wall's surface area will blow up the same way the measured perimeter does, but that;s because you've turned a boundary-length problem into the area of a different object. It still doesn't mean the country's ordinary map area becomes paradoxical, the extra boundary detail only affects a vanishingly thin strip near the edge, so the enclosed 2D area stays well behaved.